Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:

import java.util.List;
import java.util.Scanner;

public class Contest {

    //private static List<Integer> results = new ArrayList<>();
    //private static Map<Integer, List<Integer>> map = new HashMap<>();
    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String line = sc.nextLine();
        String[] split = line.split(" ");
        int n = Integer.valueOf(split[0]);

        int rc = -1;

        if (n % 2 != 0) {
            rc = (n + 1) / 2;
        } else {
            rc = (n / 2) + 1;
        }
        System.out.println(rc);
        for (int i = 1; i <= n; i++) {
            if (i % 2 != 0) {
                int var = (i + 1) / 2;
                System.out.println(String.valueOf(var) + " " + String.valueOf(var));
            } else {
                int var = (i) / 2;
                System.out.println(String.valueOf(var) + " " + String.valueOf(var + 1));
            }
        }
    }

    public static boolean isPrime(int num) {
        if (num > 2 && num % 2 == 0) {
            //System.out.println(num + " is not prime");
            return false;
        }
        int top = (int) Math.sqrt(num) + 1;
        for (int i = 3; i < top; i += 2) {
            if (num % i == 0) {
                //System.out.println(num + " is not prime");
                return false;
            }
        }
        //System.out.println(num + " is prime");
        return true;
    }

    private static void doneList(List<Integer> a) {
        StringBuilder builder = new StringBuilder("");
        for (int i = 0; i < a.size(); i++) {
            builder.append(a.get(i)).append(" ");
        }
        System.out.println(builder.toString().substring(0, builder.toString().length() - 1));
    }

    private static void doneArray(Integer[] a) {
        StringBuilder builder = new StringBuilder("");
        for (int i = 2; i < a.length; i++) {
            builder.append(a[i]).append(" ");
        }
        System.out.println(builder.toString().substring(0, builder.toString().length() - 1));
    }

    private static void done() {
        System.out.println("-1");
    }

    private static int lowerBound(int[] a, int low, int high, int element) {
        while (low < high) {
            int middle = low + (high - low) / 2;
            if (element > a[middle]) {
                low = middle + 1;
            } else {
                high = middle;
            }
        }
        return low;
    }

    private static int upperBound(int[] a, int low, int high, int element) {
        while (low < high) {
            int middle = low + (high - low) / 2;
            if (a[middle] > element) {
                high = middle;
            } else {
                low = middle + 1;
            }
        }
        return low;
    }

}